What Diffie-Hellman parameters to use? posted October 2016

I see some discussions on some mailing lists about what parameters to use for Diffie-Hellman (DH).

It seems like the recent line of papers about weak Diffie-Hellman parameters (Logjam) and Diffie-Hellman backdoors (socat, the RFC 5114, the special primes, ...) has troubled more than one.

Less than two weeks ago, a study from Dorey et al. based on these previous results was released, uncovering many problems in how Diffie-Hellman is implemented (or even backdoored!) in the wild.

This is a non-problem. We don't need a RFC to choose Diffie-Hellman groups. A simple openssl gendh -out keyfile -2 2048 will generate a 2048-bit safe prime along with correct DH parameters for you to use. If you're worried about "special primes" issues, either make it yourself with this command, or pick a larger (let's say 4096-bit safe prime) from a list and verify that it's a safe prime. You can use this tool for that.

But since some people really don't want to do the work, here are some safe parameters you can use.

2048-bit parameters for Diffie-Hellman

Here's is the .pem file containing the parameters:

-----BEGIN DH PARAMETERS-----
MIIBCAKCAQEA7WJTTl5HMXOi8+kEeze7ftMRbIiX+P7tLkmwci30S+P6xc6wG1p4
SwbpPyewFlyasdL2Dd8PkhYFtE1xD3Ssj1De+P8T0UcJn5rCHn+g2+0k/CalysKT
XrobEzihlSLeQO1NsgBt1F1XCMO+6inLVvSGVbb3Cei4q+5Djnc7Yjjq0kxGY6Hd
ds/YQnyc1xdJU8NBi3zO1XY2Uk6BSd+NN5KnLh9zRq8t/b0RiIb/fY9mJ9BCtgPo
2m4AfJE8+5dE1ttpQAJFSlA8Ku3/9Vp8sMMWATVk2Q1z9PdkikKQYRfMPYDBSIa/
8Y2l9Hh7vNYOwXd4WF5Q55RHP46RB+F+swIBAg==
-----END DH PARAMETERS-----

You can parse it yourself by piping it to openssl dh -noout -text. It uses 2 as a generator and this big hexstring as a safe prime:

ed62534e5e473173a2f3e9047b37bb7ed3116c8897f8feed2e49b0722df44be3fac5ceb01b5a784b06e93f27b0165c9ab1d2f60ddf0f921605b44d710f74ac8f50def8ff13d147099f9ac21e7fa0dbed24fc26a5cac2935eba1b1338a19522de40ed4db2006dd45d5708c3beea29cb56f48655b6f709e8b8abee438e773b6238ead24c4663a1dd76cfd8427c9cd7174953c3418b7cced57636524e8149df8d3792a72e1f7346af2dfdbd118886ff7d8f6627d042b603e8da6e007c913cfb9744d6db694002454a503c2aedfff55a7cb0c316013564d90d73f4f7648a42906117cc3d80c14886bff18da5f4787bbcd60ec17778585e50e794473f8e9107e1

4096-bit parameters for Diffie-Hellman

Here's the .pem file:

-----BEGIN DH PARAMETERS-----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-----END DH PARAMETERS-----

And here is the hexstring value of the safe prime (note that it still uses 2 as a generator):

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

Comments

John d'Oh

Why in the world would anyone sane use dh parameters from a random blog on the internets?

Jonathan

@John +1

david

Because some people just search for "what diffie hellman parameters to use" and will use the first answer they find :D

The idea here was to mix my answer with other crappy answers and broken RFCs to raise the overall security.

Blais

Because it can be useful for testing a project under development. Besides iff tgey are safe primes, which may be checked, DH relies on other parameters as the prime to be safe. DH primes are in fact so open that the different standards describe a few suggested ones. So the same way as using one from a standard one may just use any double checked prime, without having to generate it for dozens of hours.